Snapping an Extrusion
With the top face deleted and vertices selected ...


Set Pivot to Median
Set snap to Vertex and Active, and set it to influence Scale. Check 'Project on to Self'. 
With cursor close to Active (white) vertex Extrude E Scale S Limited Axis ShiftZ and snap the active vertex to the one below it.




(Holding Ctrl while dragging toggles the 'Snap' state.)